Question

A fan start rotating with constant angular acceleration of $\pi rad/s^2$ about a fixed axis perpendicular to its plane and through its centre. Find
(a) the angular velocity of the fan after $4sec$.
(b) the angular displacement of the fan after $4sec$ and
(c) number of turns accomplished by the fan in $4sec$.

Answer 1

We Know,

${\omega }_f={\omega }_i+\alpha t$

${\theta }_f={\theta }_i+\frac{1}{2}\alpha t^2$

$\text{(a)}$. ${\omega }_f=0+\pi \times 4=4\pi rad/s$

$\text{(b)}$.${\theta }_f-{\theta }_i=\frac{1}{2}\pi \times 16=8\pi rad$

$\text{(c)}$. After 4 sec angular displacement $=8\pi$

$\text{No. of turns}=\frac{\text{angular displacement}}{2\pi }$

$\text{No. of turns}=\frac{8\pi }{2\pi }=4turns$